1. **State the problem:** Solve the equation $$(x - 2)^2 = (x + 7)^2 - 3x$$ 2. **Recall the formula:** The square of a binomial is $$(a \pm b)^2 = a^2 \pm 2ab + b^2$$ 3. **Expand both sides:** $$(x - 2)^2 = x^2 - 4x + 4$$ $$(x + 7)^2 = x^2 + 14x + 49$$ 4. **Rewrite the equation:** $$x^2 - 4x + 4 = x^2 + 14x + 49 - 3x$$ 5. **Simplify the right side:** $$x^2 - 4x + 4 = x^2 + 11x + 49$$ 6. **Subtract $x^2$ from both sides:** $$-4x + 4 = 11x + 49$$ 7. **Bring all terms to one side:** $$-4x - 11x + 4 - 49 = 0$$ $$-15x - 45 = 0$$ 8. **Solve for $x$:** $$-15x = 45$$ $$x = \frac{45}{-15} = -3$$ **Final answer:** $$x = -3$$